The purpose of this project is development of biostatistical methods and mathematical models appropriate for the analysis of epidemiologic and experimental studies related to cancer control and prevention. Many of the statistical problems being studied under this project are derived from the consultation activities of the Section. The proper time metric to be used when applying Cox regression techniques to analyze a cohort's cancer incidence over time is being studied by simulation methods. Data are being generated according to known cancer age-specific incidence and known mortality from all causes. The time metrics being studied are follow-up time from study initiation and age at risk. Different study durations are also being evaluated. In addition, different methods to properly estimate the effect of risk factors which are related to age at ascertainment are being evaluated. The assumption of "proportional hazards" is commonly made when analyzing survival in patients treated for cancer. The scale parameter in parametric models and the underlying hazard function in semi-parametric models are assumed to vary between patients only because of the risk factors included in the model. However, extraneous hazard rate heterogeneity can produce substantial deviations from this assumption. This research will fit a Gamma-mixture of Weibull models to estimate the degree of heterogeneity and its biasing effect on estimated parameters and on the hazard ratio. Methodology is being developed to calculate the necessary sample size n,m (n is the number of measuring devices and m is the number of items being measured) to test the hypothesis that the accuracy of a measuring device is acceptably large. The results will be used to develop sampling methods to evaluate the accuracy of the CIS.